problem 13 14 in julia

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+###
+# Longest Collatz sequence
+# Problem 14
+#
+# The following iterative sequence is defined for the set of positive integers:
+# n → n/2 (n is even)n → 3n + 1 (n is odd)
+# Using the rule above and starting with 13, we generate the following sequence:
+# 13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1
+# It can be seen that this sequence (starting at 13 and finishing at 1) contains 10 terms.
+# Although it has not been proved yet (Collatz Problem), it is thought that all starting
+# numbers finish at 1.
+# Which starting number, under one million, produces the longest chain?
+# NOTE: Once the chain starts the terms are allowed to go above one million.
+###
+
+function collatz_length(n)
+    n == 1 && return 1
+    n % 2 == 0 && return 1 + collatz_length(n ÷ 2)
+    return 1 + collatz_length(3n + 1)
+end
+
+result = argmax([collatz_length(x) for x in 1:(1_000_000 - 1)])
+
+println(result)